404 when trying to access servlet

Hello, I've been trying to learn to use servlets but I've unfortunately hit a roadblock. I'm pretty sure I've defined by web.xml correctly, but I'm getting a 404 when I try to access my servlet. I can go to index.jsp just fine, but not any of the servlets that I've tried. I'm using Tomcat and Eclipse, if it matters. No errors appear in the tomcat logs.

I guess the weird thing is that this behavior seems to be inconsistent. The 404 happens when I deploy the application by creating an XML file with a docBase and a path in TOMCAT_HOME\conf\Catalina\localhost. However, when I use the Eclipse plugin to deploy the app (the plugin points to the same TOMCAT_HOME above) or if I build a war file and drop it into TOMCAT_HOME\webapps, the above behavior is reversed. I can access the servlet but not any of my static files (JSPs, HTMLs, etc.). Has anyone encountered this behavior? I've been stuck for days.